OrderedSet

catdef.spad line 1027 [edit on github]

The class of totally ordered sets, that is, sets such that for each pair of elements (a, b) exactly one of the following relations holds a<b or a=b or b<a and the relation is transitive, i.e. a<b and b<c => a<c. This order should be the natural order on given structure.

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

latex: % -> String

from SetCategory

max: (%, %) -> %

max(x,y) returns the maximum of x and y relative to "<".

min: (%, %) -> %

min(x,y) returns the minimum of x and y relative to "<".

negative?: % -> Boolean if % has SetWithZero

negative?(x) tests whether x is strictly less than 0.

positive?: % -> Boolean if % has SetWithZero

positive?(x) tests whether x is strictly greater than 0.

sign: % -> Integer if % has SetWithZero

sign(x) is 1 if x is positive, -1 if x is negative, 0 if x equals 0.

smaller?: (%, %) -> Boolean

from Comparable

BasicType

CoercibleTo OutputForm

Comparable

PartialOrder

SetCategory